No no no. Everything you are describing is what, for the most part, caused 9/11.
I recommend reading against all enemies, because I really hope you and we as a nation can learn from our mistakes. We certainly aren't doing it.
The Middle East isn't a chessboard like the way most politicians saw it during the cold war. This ideology created a lot of very harmful things, including a majority of the fundamentalist movements. Israelis deserve better than what we have given them. We have given them nuclear capabilities, an absurd amount of military technology, enough guns to fight off the entire Middle East, and did you know we still give Egypt billions of dollars for no reason other than to uphold a treaty to not attack Israel (camp david accords 1979). Now Israeli technology has probably surpassed ours in most areas. They are no longer the defenseless country that once was but now a victim of their own circumstances and a complete aggressor. One which we essentially propped up because we saw it as a friendly ally.
Also it is absurd to say that the Middle East has always been "chaos". It has been chaos ever since the west got involved. Much like Africa, drawing lines in the sand doesn't constitute a division of ethnicity like it works out oh so perfectly in the developed world. Look at where the civilized world originated, where mathematics originated, etc.
Let it be a lesson to anyone else who has misconceived notions of the Middle East, the way we are dealing with it now only creates a perpetual problem. The hole we dug ourselves is deep, but not impossible to climb out of.